Libyan Deputy Foreign Minister Abdelati Obeidi told Greek Prime Minister George Papandreou on Sunday that Libya wants to end fighting in the country, Greek officials said.
"It seems that the Libyan authorities are seeking a solution," Foreign Minister Dimitris Droutsas said after the envoy met Papandreou. "There needs to be a serious effort for peace and stability in the region."
A Greek government official told Reuters that Obeidi had said Libya wanted the fighting to end. Obeidi told Papandreou he will next travel to Malta and Turkey, Droutsas added.
A senior Greek government official earlier said that Obeidi had arrived in Athens to deliver a message from Libyan leader Muammar Gaddafi to the Greek Prime Minister.
In Tripoli, Libyan officials were not immediately available to comment on Obeidi's movements.
He served as prime minister under Libyan leader Muammar Gaddafi in the late 1970s, and later was head of the General People's Congress, or parliament. His current post is minister of state for European affairs.
Last week Libyan Foreign Minister Moussa Koussa crossed into Tunisia and then flew from Djerba airport to southern England. The British government said he had defected.
Kussa could hold the key to persuading other key regime figures to turn their back on Gaddafi, analysts said Sunday.
But they warned that the Libyan leader's close-knit inner circle of family and clan members is unlikely to be brought down by the defection of a handful of ministers.
Kussa apparently surprised Libya and the West when he touched down at Farnborough Airport southwest of London on Wednesday and announced he was resigning his role.
The man seen as a close confidante of Gaddafi is now reportedly being debriefed by British intelligence agents at a safe house.
He has not been seen in public and there has been no indication of how long he intends to stay or why he chose to come to Britain.
Dr Alia Brahimi, Global Security Research Fellow at the London School of Economics, said Kussa's defection will show others "that people very close to Kadhafi have made the judgement that this is a sinking ship and it's time to defect now."
Brahimi said high-profile figures such as Kussa who were involved in bringing Libya back into the international fold in the last decade will conclude that he has deserted the Libyan leader because he sees a grim future even if the regime defeats the rebel insurgency.
"We can assume there would be number of those people around him that would perhaps make a similar judgement: that even if Kadhafi wins, Libya would go back to the years of isolationism when life was very, very hard," she told AFP.
However, Kussa's defection has coincided with a series of reverses for the rebels, who have been forced into retreat as the better-organised pro-Kadhafi forces have fought back despite coming under continued Western air strikes.
Shashank Joshi, an associate fellow at London-based military think-tank, the Royal United Services Institute (RUSI), said that while the defection is significant, it does not necessarily follow that the regime is falling apart.
"This sends a long-term signal and it will make other Arab countries who may have been backing Kadhafi think twice," he told AFP.
"But Libya is highly clan-based and family-based. At the core of it is a connection between Kadhafi and his clan, like a spinal cord."
The regime is now focused on the war, Joshi said, "and so the defection of an oil minister would not be the end of the world."